Destructive items are exclusive to Zombie Slayer so you won't see them in any other games.
These items are not armable or craftable, but will give you a one-time extra advantage in Fights. You can view your Destructives by selecting "Destructives" from the drop down menu on your Inventory page.

You're also able to view the effect Destructives had on a fight by clicking fight details; it'll show you what destructive was consumed and whether or not it was stronger or weaker than the destructive used by your opponent.